On this week’s edition of “Fox News Sunday,” Texas Rep. Ron Paul put rumors of a third-party presidential run to rest, saying he had no interest in running as a third party candidate. But that doesn’t mean he would support the eventual GOP nominee.

Speculation about that potential endgame has swirled since Rep. Paul first announced that he would not be running for re-election to Congress.

“Probably not unless I get to talk to them and find out what they believe in,” Paul said of whether he would support the Republican nominee — presuming it’s not him.

“But if they believe in expanding the wars, if they don’t believe in looking at the Federal Reserve, if they don’t believe in real cuts, if they don’t believe in deregulation and a better tax system, it would defy everything I believe in. And so therefore I would be reluctant to jump on board and tell all of the supporters that have given me trust and money, then all of a sudden say, ‘All we have done is for naught and let’s support anybody at all because even if they disagree with everything we do.’”

The Texas congressman told Fox’s Chris Wallace that he just doesn’t want to do mount a third-party challenge.

WALLACE: Does that mean you might then consider an independent run?
PAUL: No, doesn’t mean that at all.
WALLACE: Would you?
PAUL: I have no intention doing that. That doesn’t make any sense to me — to even think about it, to let alone plan to do that.
WALLACE: Because?
PAUL: Because I don’t want to do it. That’s a pretty good reason.